The prior art knows methods in which an operating variable of a burner, e.g. the air ratio λ, is determined by measuring an ionization current flowing off the ionization electrode introduced into the combustion zone. Here, an alternating voltage is applied to the ionization electrode and a current which flows off the ionization electrode and is rectified due to the rectifying property of the flame is detected as the ionization current. Then, the measured ionization current is compared by means of a control circuit with a set point for the ionization current that corresponds to the adjusted set point of the air ratio, and the composition of the air-fuel mixture is appropriately corrected. Such a method is described in document DE 44 33 425 A1, for example. At the same time, it is known how to detect the presence of a flame in the combustion zone by means of an ionization current measurement or flame resistance measurement.
However, the problem of these previously known methods is that the control circuit has a fixed measurement resolution while the detected ionization current progresses in a non-linear fashion over its modulation range. Therefore, it is not possible to detect the ionization current or flame resistance at a plurality of operating points of the burner with the measurement resolution which is optimal for each operating point.